Two to three hours before cooking, bring the rib roast to room temperature. Remove the roast from the fridge. Evenly coat the roast with the oil, salt, pepper. Massage the seasonings into the meat. Set aside.
When ready to cook, place the butter into the Instant Pot. Using the sauté feature, melt the butter. Add the shallot, garlic and softened, about 4 minutes. Add the tomato paste and sauté for 1 to 2 minutes or until the tomato paste begins to brown and stick to the bottom of the pan. Stir frequently.
Deglaze the pan with water and red wine. Scrape up any remaining brown bits.
Place the rib roast inside the Instant Pot. Secure the lid and cook on high pressure for 50 minutes. If you have a smaller rib roast, cook for 50 minutes. Turn off the Instant Pot and let rest for 20 minutes. Release the pressure naturally and remove the roast.
In a large skillet, add 2 tablespoons of butter and warm over high heat. Once the pan is hot, sear all sides of the rib roast, about 1 1/2 minutes per side. Place the rib roast on a rimmed cutting board. Pour the cooking liquid from the Instant Pot into the skillet. Deglaze the skillet and let the sauce simmer for 5 minutes. Taste and adjust with salt and pepper.
Slice the rib roast and drizzle with the pan sauce onto the meat. Serve with an optional Horseradish Cream Sauce.